Getting Started 
Misconception/Error The student confuses values of the independent variable with values of the dependent variable. 
Examples of Student Work at this Level The student circles the point (2, 3) and says that f (3) = 2, f (3) = (2, 3), or never clearly identifies the value of f (3).

Questions Eliciting Thinking What is the difference between values of the independent variable and values of the dependent variable?
Which axis corresponds to the inputs (or values of the independent variable)? Which axis corresponds to the outputs (or values of the independent variable)?
In the expression fÂ (3), is three an input or an output? What is the significance of f? 
Instructional Implications Review the concept of a function and provide instruction on function notation. Present functions in a variety of ways, using verbal descriptions, graphs, algebraic rules, and tables. Assist the student in identifying and distinguishing between values of the independent and dependent variables in each of the various ways that functions might be presented. Use function notation to refer to values of the dependent variable. Given a function f (presented as a verbal description, graph, algebraic rule, or table) pose problems such as the following: (1) Identify the value of fÂ (2) and (2) Find the value of x suchÂ that fÂ (x) = 7.
Consider implementing MFAS tasks What Is the Value? (FIF.1.2), Evaluating a Function (FIF.1.2), and Cell Phone Battery Life (FIF.1.2). 
Moving Forward 
Misconception/Error The student is able to identify the point that corresponds to fÂ (3) but cannot clearly identify the value of fÂ (3). 
Examples of Student Work at this Level The student circles the point whose coordinates are (3, 4) but cannot clearly identify the value of f (3). For example, the student:
 Says the value of fÂ (3) is (3, 4).
 Describes the coordinates of the point (3, 4) in context without clearly identifying the value of f (3).
 Only identifies the xcoordinate associated with fÂ (3).

Questions Eliciting Thinking Can you explain in words what fÂ (3) refers to?
How would you describe the point that you circled? Can you write that using function notation?
If x = 3, what is the value of fÂ (3)? 
Instructional Implications Review function notation. Make explicit that fÂ (a) refers to the value of the dependent variable that corresponds to x = a. Assist the student in correcting his or her identification of fÂ (3) and in representing this identification by writing fÂ (3) = 4. Provide additional examples of graphed functions and ask the student to find specific values of variables given their corresponding independent or dependent variable values. Provide feedback as needed.
Consider implementing MFAS tasks What Is The Value? (FIF.1.2), Evaluating a Function (FIF.1.2), and Cell Phone Battery Life (FIF.1.2). 
Almost There 
Misconception/Error The student is unable to clearly explain the identification of the value of fÂ (3). 
Examples of Student Work at this Level The student circles the point whose coordinates are (3, 4) and clearly identifies the value of fÂ (3) as 4. However, when justifying the identification, the student:
 Imprecisely explains how to locate the ycoordinate of the point whose xcoordinate is three.
 Simply says it is on the graph.
 Uses terminology incorrectly, for example, refers to f (3) as a value of the independent variable.

Questions Eliciting Thinking How did you use the graph to find the value of fÂ (3)?
What does a function do to inputs and outpoints?
For the point (3, 4), which coordinate is the input (or a value of the independent variable) and which is the output (or a value of the dependent variable)? 
Instructional Implications Model explaining why fÂ (3) = 4 using the terminology of functions. Explain to the student that it is not necessary to describe the details of using the graph to locate the point (3, 4). Emphasize that fÂ (3) = 4 since four is the value of the dependent variable (or element of the range) that corresponds to the independent variable value, x = 3, and that this can be determined by finding the ycoordinate of the point on the graph whose xcoordinate is three.
Consider implementing MFAS tasks What Is The Value? (FIF.1.2), Evaluating a Function (FIF.1.2), and Cell Phone Battery Life (FIF.1.2). 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student correctly identifies the point that corresponds to fÂ (3) and states that fÂ (3) = 4. The student explains that fÂ (3) represents the output (or element from the range) that corresponds to the input (or domain element) x = 3.

Questions Eliciting Thinking Can you write the ordered pair that corresponds to this point?
Which value represents the independent variable? Which value represents the dependent variable?
What is the value of x if fÂ (x) = 7? 
Instructional Implications Provide the student with problems involving graphs of two functions, f and g. Then ask the student to find the value of, for example, fÂ (4) + gÂ (5) or (f + g)(6).
Consider implementing MFAS tasks What Is the Value? (FIF.1.2), Evaluating a Function (FIF.1.2), and Cell Phone Battery Life (FIF.1.2). 